Final Exam: Chapters 14+15

Question 1

A wave trave;s along a stretched horizontal rope. The vertical distance from crest to trough for this wave is 13cm and the horizontal distance from crest to trough is 28cm. What is the wavelength and amplitude of this wave?

Wavelength= Distance from crest to crest

Amplitude= Half distance from the bottom of the wave to the top

Answer 1

Wavelength= 2(.28)

Wavelength= 0.56m

Amplitude= (1/2)(.13)

Amplitude= 0.065m

Question 2

A 4.5Hz wave with an amplitude of 12cm and a wavelength of 27cm travels along a stretched horizontal string. How far does a given peak on the wave travel in a time inerval of 0.50 seconds? How far does a knot on the string travel in the same time interval? How would your answers to parts a+b change if the amplitude of the wave were halved?

Velocity= d/t

Distance= vt

Velocity= (f)(y)

y used as lambda

1 period travels up and down a distance of 4 times

Answer 2

Distance= (f)(y)(t)

Distance= (4.5)(0.027)(0.50)

Distance= 0.61m

Distance of knot: (4A)(1/T)

Distance of knot= (4A)(f)(t)

Distance of knot: (4)(0.012)(4.5)(0.5)

Distance of knot= 1.1m

Question 3

Two steel guitar strings have the same length. String A has a diameter of 0.5mm and is under 410N of tension. String B has a diameter of 1mm and is under a tension of 820N. Find the ratio of the wave speeds, Va/Vb in these two strings.

V= sqrt(F/u)

V= sqrt(FpA)

V= sqrt(Fπ(d/2²))

V= sqrt(F) x (d)

Answer 3

(Va/Vb)= sqrt(410/820) x (1/0.5)

= sqrt(2)

= 1.4

Refer to picture solution

Question 4

A wave on a string is described by the following equation

y= (15cm)cos(π/5cm(X)) - (π/12sec)t

What is the amplitude of this wave? What is its wavelength? What is its period? In what diresction does the wave travel?

Y= Acos(2π/y)(x) - (2π/T)(t)

Answer 4

Question 5

Two wave pulses on a string approach one another at the time t=0. Each pulse moves with a speed of 1 m/s. Make a careful sketch of the resultant wave at the times t= 1sec, 2sec, 2.5sec, and 4sec, assuming that the perposition principal holds for these waves.

Answer 5

Question 6

An organ pipe that is open at both ends is 3.5m long. What is its fundamental frequency?

Answer 6

Question 7

A string 1.5m long with a mass of 2.6g is stretched between two fixed points with a tension of 93N. Find the frequency of the fundamental on this string.

Answer 7

Question 8

The organ pipe is 2.75m long. What is the frequency of the standing wave shown in the pipe? What is the fundamental frequency of this pipe?

Answer 8

Question 9

The frequency of the standing wave shown is 202Hz. What is the fundamental frequency of this pipe? What is the length of this pipe?

Answer 9